10 papers · 1 filter
On the Turán number of the expansion of the book
Xin Cheng, Dániel Gerbner, Hilal Hama Karim
The book with pages is the graph on vertices consisting of triangles which intersect at exactly one common edge. For a given graph , the -expansion of …
On oriented Turán problems
Dániel Gerbner, Xuanrui Hu, Yuefang Sun
The oriented Turán number of a given oriented graph , denoted by $\exo(n,\overrightarrow{F})$, is the largest number of arcs in -vertex -…
On Turán problems for Berge forests
Junpeng Zhou, Dániel Gerbner, Xiying Yuan
For a graph , an -uniform hypergraph is a Berge- if there is a bijection such that for each . Given a family $\ma…
Survey of generalized Turán problems -- counting subgraphs
Dániel Gerbner, Cory Palmer
For fixed graphs and , the \emph{generalized Turán number} is the maximum possible number of copies of a subgraph in an -vertex -free graph. T…
On the Turán number of the expansion of the -fan
Xin Cheng, Dániel Gerbner, Hilal Hama Karim +1
The -fan is the graph on vertices consisting of triangles which intersect at exactly one common vertex. For a given graph , the -expansion of is the $…
On Turán problems for suspension hypergraphs
Xin Cheng, Dániel Gerbner, Hilal Hama Karim +1
For a given graph , the -uniform suspension of is the -uniform hypergraph obtained from by taking new vertices and adding them to every edge. In this paper,…
On Turán-type problems and the abstract chromatic number
Dániel Gerbner, Hilal Hama Karim, Gaurav Kucheriya
In 2020, Coregliano and Razborov introduced a general framework to study limits of combinatorial objects, using logic and model theory. They introduced the abstract chromatic numbe…
On hypergraph Turán problems with bounded matching number
Dániel Gerbner, Casey Tompkins, Junpeng Zhou
Very recently, Alon and Frankl, and Gerbner studied the maximum number of edges in -vertex -free graphs with bounded matching number, respectively. We consider the analogous…
Generalized Turán results for matchings
Dániel Gerbner
Given graphs and , the generalized Turán number is the largest number of copies of in -vertex -free graphs. We study the case when either …
Generalized regular Turán numbers
Dániel Gerbner, Hilal Hama Karim
We combine two generalizations of ordinary Turán problems. Given graphs and and a positive integer , we study , which is the largest number of copies of $…